A BIFURCATION PHENOMENON FOR A DIRICHLET PROBLEM WITH AN EXPONENTIAL NONLINEARITY

A nonlinear Dirichlet boundary value problem Δu + λeu = 0 in bounded, simply connected domains in R2 is considered. The Weston-Moseley theory yields a method to construct "large solutions" of the above problem from the roots of a certain equation associated with the domain. An application of the Golubitsky-Schaeffer bifurcation theory clarifies the bifurcation phenomena of those roots as the domain varies, which leads to the bifurcation of solutions of our problem. © 1991.